Weekly Papers on Quantum Foundations (19)

Page-Wootters formulation of indefinite causal order. (arXiv:2105.02304v1 [quant-ph])

上午9:33|Veronika Baumann, Marius Krumm, Philippe Allard Guérin, Časlav Brukner|quant-ph updates on arXiv.org

One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix framework. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several observers, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such observers with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the physical implementation of process matrices and on the perspectives of the observers as described via causal reference frames. While it allows for describing scenarios where different definite causal orders are coherently controlled, we explain why certain non-causal processes might not be implementable within this setting.

Consciousness and the Collapse of the Wave Function. (arXiv:2105.02314v1 [quant-ph])

上午9:33|David J. Chalmers, Kelvin J. McQueen|quant-ph updates on arXiv.org

Does consciousness collapse the quantum wave function? This idea was taken seriously by John von Neumann and Eugene Wigner but is now widely dismissed. We develop the idea by combining a mathematical theory of consciousness (integrated information theory) with an account of quantum collapse dynamics (continuous spontaneous localization). Simple versions of the theory are falsified by the quantum Zeno effect, but more complex versions remain compatible with empirical evidence. In principle, versions of the theory can be tested by experiments with quantum computers. The upshot is not that consciousness-collapse interpretations are clearly correct, but that there is a research program here worth exploring.

The EPR paper: a pedagogical approach. (arXiv:2105.02384v1 [quant-ph])

上午9:33|Angel Garcia-Chung|quant-ph updates on arXiv.org

On the seminal paper written by Einstein, Podolsky and Rosen [1], a critique to the completeness of quantum mechanics was posed. Part of the critique consisted in the following argument: if quantum mechanics is complete, then, two physical quantities, with non-commuting operators, can have simultaneous reality. In this paper I aim to provide a pedagogical approach to the notions used in the EPR’s argument.

Schrodinger’s Equation is Universal, Dark Matter and Double Diffusion. (arXiv:2105.02690v1 [cond-mat.stat-mech])

上午9:33|Johan Beumee, Hershel Rabitz|quant-ph updates on arXiv.org

This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum while ignoring the angular momentum, spin or other particle characteristics. The main result of the paper shows that the colliding two particle classical Hamiltonian energy can be represented in four weighted individual particle in symmetric and anti-symmetric (osmotic) terms similar to the quadratic Nelson measure used in the derivation of the Schrodinger wave function. Following Nelson, if the second particle behavior can be captured in a potential and the ingoing and outgoing velocities of the main particle are modelled using stochastic differential equations the motion of the main particle satisfies the Schrodinger’s equation. The diffusion variance of this equation is replaced by a related ratio of masses and the assumed variance. The first example attempts to reconcile this result with quantum mechanics by considering the Schrodinger equation in the presence of only one type of incident particle. The main particle energy levels become multiples of the incident particle and the energy expression for the entire system agrees with quantum mechanics but there are differences with the stochastic equation. The Schrodinger equation can also be used to represent corrections for Newton’s equation and suggests a user profile to be used in the search for Dark Matter. An alternative solution to the collision model also shows relativistic properties as the interactions suggest corrections to the Minkowski equation in Einstein’s Special Relativity. It is also possible to use the classical Schrodinger’s equation both on the main and incident particle simultaneously leading to a correlated set of wave equations with different diffusion parameters.

A Grand Unification of Quantum Algorithms. (arXiv:2105.02859v1 [quant-ph])

上午9:33|John M. Martyn, Zane M. Rossi, Andrew K. Tan, Isaac L. Chuang|quant-ph updates on arXiv.org

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW’19 paper on QSVT [Gily\’en, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW’19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.

Fundamental weight systems are quantum states. (arXiv:2105.02871v1 [math.GT])

上午9:33|David Corfield, Hisham Sati, Urs Schreiber|quant-ph updates on arXiv.org

Weight systems on chord diagrams play a central role in knot theory and Chern-Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagrams is canonically a star-algebra, and ask which weight systems are positive with respect to this structure; hence we ask: Which weight systems are quantum states, if horizontal chord diagrams are quantum observables? We observe that the fundamental gl(n)-weight systems on horizontal chord diagrams with N strands may be identified with the Cayley distance kernel at inverse temperature beta=ln(n) on the symmetric group on N elements. In contrast to related kernels like the Mallows kernel, the positivity of the Cayley distance kernel had remained open. We characterize its phases of indefinite, semi-definite and definite positivity, in dependence of the inverse temperature beta; and we prove that the Cayley distance kernel is positive (semi-)definite at beta=ln(n) for all n=1,2,3,… In particular, this proves that all fundamental gl(n)-weight systems are quantum states, and hence so are all their convex combinations. We close with briefly recalling how, under our “Hypothesis H”, this result impacts on the identification of bound states of multiple M5-branes.

Anisotropic Multiverse with Varying $c$, $G$ and Study of Thermodynamics. (arXiv:2105.02687v1 [gr-qc])

上午9:33|gr-qc updates on arXiv.org

Authors: Ujjal DebnathSoumak Nag

We assume the anisotropic model of the Universe in the framework of varying speed of light $c$ and varying gravitational constant $G$ theories and study different types of singularities. For the singularity models, we write the scale factors in terms of cosmic time and found some conditions for possible singularities. For future singularities, we assume the forms of varying speed of light and varying gravitational constant. For regularizing big bang singularity, we assume two forms of scale factors: sine model and tangent model. For both the models, we examine the validity of null energy condition and strong energy condition. Start from the first law of thermodynamics, we study the thermodynamic behaviours of $n$ number of Universes (i.e., Multiverse) for (i) varying $c$, (ii) varying $G$ and (iii) both varying $c$ and $G$ models. We found the total entropies for all the cases in the anisotropic Multiverse model. We also found the nature of the Multiverse if total entropy is constant.

De Sitter space-times in Entangled Relativity. (arXiv:2011.14633v2 [gr-qc] UPDATED)

上午9:33|gr-qc updates on arXiv.org

Authors: Olivier Minazzoli

It is argued that de Sitter space-times might be solutions of entangled relativity once the quantum trace anomaly from matter fields in curved space-times is taken into account. This hypothesis would be an elegant solution to the acceleration of the expansion of the universe within the rigid framework of entangled relativity.

Varieties of Dispositional Essentialism about Natural Laws

2021年5月6日 星期四 上午9:00|Philsci-Archive: No conditions. Results ordered -Date Deposited.

Hirèche, Salim (2020) Varieties of Dispositional Essentialism about Natural Laws. [Preprint]

Lost Horizon? – Modeling Black Holes in String Theory

2021年5月4日 星期二 下午3:25|Philsci-Archive: No conditions. Results ordered -Date Deposited.

Huggett, Nick and Matsubara, Keizo (2020) Lost Horizon? – Modeling Black Holes in String Theory. [Preprint]

Epistemic Modality, Mind, and Mathematics

2021年5月4日 星期二 下午3:24|Philsci-Archive: No conditions. Results ordered -Date Deposited.

Khudairi, Hasen (2017) Epistemic Modality, Mind, and Mathematics. [Preprint]

The Math is not the Territory: Navigating the Free Energy Principle

2021年5月4日 星期二 上午7:25|Philsci-Archive: No conditions. Results ordered -Date Deposited.

Andrews, Mel (2021) The Math is not the Territory: Navigating the Free Energy Principle. [Preprint]

Feyerabend’s rule and dark matter

2021年5月3日 星期一 上午8:00|Latest Results for Synthese

Abstract

Paul Feyerabend argued that theories can be faced with experimental anomalies whose refuting character can only be recognized by developing alternatives to the theory. The alternate theory must explain the experimental results without contrivance and it must also be supported by independent evidence. I show that the situation described by Feyerabend arises again and again in experiments or observations that test the postulates in the standard cosmological model relating to dark matter. The alternate theory is Milgrom’s modified dynamics (MOND). I discuss three examples: the failure to detect dark-matter particles in laboratory experiments; the lack of evidence for dark-matter sub-haloes and the dwarf galaxies that are postulated to inhabit them; and the failure to confirm the predicted orbital decay of Milky Way satellite galaxies and other systems due to dynamical friction against the dark matter. In each case, Feyerabend’s criterion directs us to interpret the experimental or observational results as an indirect refutation of the standard cosmological model in favor of Milgrom’s theory.

Thinking about Progress: From Science to Philosophy

2021年5月3日 星期一 上午1:40|Philsci-Archive: No conditions. Results ordered -Date Deposited.

Dellsén, Finnur and Lawler, Insa and Norton, James (2021) Thinking about Progress: From Science to Philosophy. [Preprint]

Philosophy in Science: Can philosophers of science permeate through science and produce scientific knowledge?

2021年5月1日 星期六 下午5:18|Philsci-Archive: No conditions. Results ordered -Date Deposited.

Pradeu, Thomas and Lemoine, Maël and Khelfaoui, Mahdi and Gingras, Yves (2021) Philosophy in Science: Can philosophers of science permeate through science and produce scientific knowledge? [Preprint]

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